Is this Texas mother a victim or a murderer?

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Photos:'Death Row Stories': Darlie Routier

A family photo shows Darlie Routier; her husband, Darin; and their sons Damon and Devon. On June 6, 1996, both children were brutally stabbed to death in their Dallas-area home. Darlie Routier's throat was slashed that night; a necklace she had been wearing apparently saved her life as it stopped the knife from hitting her carotid artery.

Within days, police arrested Darlie Routier and charged her with the two boys' murders. She was convicted and sentenced to death. To date, she has steadfastly claimed a home intruder was responsible for the attack and that she is innocent.

Twelve days after the murders, Darlie and Darin Routier returned to the police department voluntarily for another round of questioning. Only one of them would walk out: Darlie Routier was arrested on June 18, 1996, by the Rowlett, Texas, Police Department.

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Photos:'Death Row Stories': Darlie Routier

Darlie Routier was a 26-year-old mother of three boys at the time of the killings. Here, she's seen in a family photo with the slain Devon and Damon. Drake, the third son, who was an infant at the time of the murders, was asleep upstairs and was not injured.

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Photos:'Death Row Stories': Darlie Routier

A photo of the crime scene shows the cordless telephone Darlie Routier used to call 911 on the night of the attacks. The 911 recording and the duration of the call (five minutes and 42 seconds) were key pieces of evidence during the trial.

Appellate lawyer Stephen Cooper would later argue that given the length of time Routier was on the phone with 911, the prosecution's timeline of events was flawed: One piece of evidence was a sock with both boys' blood on it that was found in an alley 75 yards away from the house.

"There is not but a couple of minutes for her to stab and kill the children, cut the screen, get this sock and run it down the alley in the dark through a gate that doesn't really work very well, (and) come back," Cooper said.

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Photos:'Death Row Stories': Darlie Routier

Police alleged that Routier had stabbed her boys with a kitchen knife pulled from this kitchen block.

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Photos:'Death Row Stories': Darlie Routier

An evidence photo shows 5-year-old Damon's bloody handprint. He had been stabbed multiple times in the back.

During the initial questioning, when she'd regained consciousness after surgery in the hospital for her injuries, Routier told police she woke up to a man standing over her and there was a physical struggle. Later, when she was brought into the police department for questioning, she said she awoke to Damon, dripping with blood, calling out, "Mommy! Mommy!"

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Photos:'Death Row Stories': Darlie Routier

In court, prosecutors argued that Routier had fabricated the story of an assailant, because valuable jewelry had been left untouched on the kitchen counter.

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The prosecution would later use this as a key piece of evidence against Routier, as well as the fact that valuable jewelry was left on the counter in plain sight and untouched. Prosecutors also pointed out that Routier, at one point in the 911 call, was worried about touching the knife.

"God ... I bet if we could have gotten the prints maybe," she told the 911 operator.

Perhaps the most damning piece of evidence was a video of Routier, just eight days after the attack, smiling, singing "Happy Birthday" and shooting Silly String on her sons' grave site.

Building the appeal

Soon after, appellate attorney Stephen Cooper was assigned to the case and made a shocking discovery: Court reporter Sandra Halsey had made more than 30,000 mistakes in the trial transcript. Forty to 50% of those were "substantial," Kathy Cruz said.

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Without a reliable transcript, Cooper couldn't stage a proper appeal. He felt the substantiated errors would earn Routier a new day in court, yet her motion for a new trial was denied.

Instead, the state offered her life in prison if she dropped her appeal and admitted to her children's murder. Routier refused.

Cooper says he also came across game-changing pieces of evidence that the jury didn't see.

"What was not shown the jury was this two-hour memorial video that took place before the Silly String incident," Cooper said.

Also unseen: photos of Routier's extensive wounds and bruises which, in her attorney's eyes, cast doubt on whether her injuries could have been self-inflicted.

Cooper also questioned why Routier's husband was not investigated more thoroughly. In a signed affadavit, he admitted to one insurance scam as well as a plot for a staged home robbery so he could collect a claim. Darin Routier would have collected on his wife's life insurance had she died of her injuries.

Darin Routier denied involvement in the murders, and subjected himself to a polygraph test by Brian Pardo, a wealthy businessman who had become interested in the case.

He failed.

"Darlie had no motive at all, and Darin had $250,000 worth of motive," Pardo said.

Questioning the timeline

Still, most look at a bloody boy's sock found in an alley 75 yards away from the home as what could ultimately help free Routier.

"That sock is the most important piece of evidence in this entire case," Cruz said.

Cooper argues it's nearly impossible for her to have had enough time to stab the two boys, call 911, cut the screen in her home, run the sock down an alley and come back and inflict her own wounds.

Victim or perpetrator?

Routier asserts her innocence to this day and waits on death row for her appeal to move forward. She and her husband divorced in 2011. Darin Routier currently lives in Lubbock, Texas, with their surviving son, Drake.

Tune in to "Death Row Stories," Sunday at 10 p.m. ET/PT to see all the evidence of the case against Darlie Routier.